A right pyramid stands on a rectangular base whose sides are 24 cm and 18 cm and each of the slant edge is 17 cm. Find the height and the volume of the pyramid.
OPtion
1) 12 cm and 1252 cm^3
2) 12 cm and 1164 cm^3
3) 10 cm and 1164 cm^3
4) 10 cm and 1254 cm^3
5) 6 cm and 1450 cm^3
6) 6 cm and 1152 cm^3
7) 6 cm and 1120 cm^3
8) 8 cm and 1152 cm^3
9) 8 cm and 1164 cm^3
10)8 cm and 1252 cm^3
Solution
By using figure
AB = 25 cm (base one side)
AD = 18 cm (base other side)
AS = 17 cm (slant edge)
Now
AO = Sqrt (AP^2 + OP^2) = Sqrt (9^2 + 12^2) = 15 cm (O is base centre and P is AD centre)
AS^2 = AO^2 + OS^2 (S is top point of pyramid)
then OS = Sqrt 64 = 8
height = 8
Volume = 1/3*18*24*8 = 1152 cm^2
Option 8)
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